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Evaluation of Uncertainties and Risks in Geology: New by Professor Dr. György Bárdossy, Professor Dr. János Fodor PDF

By Professor Dr. György Bárdossy, Professor Dr. János Fodor (auth.)

ISBN-10: 3642058337

ISBN-13: 9783642058332

ISBN-10: 366207138X

ISBN-13: 9783662071380

High degrees of uncertainty are an indicator of geological investigations, resembling the hunt for oil, diamonds, and uranium. So enterprise ventures regarding geology, corresponding to mineral exploration and mining, are obviously linked to better dangers than extra conventional entrepreneurial ventures in and economic climate. There also are a few risky traditional dangers, e.g. earthquakes, volcanic actions, and inundations, which are the direct results of geological tactics. it truly is of paramount curiosity to check all of them, to explain them, to appreciate their foundation and - if attainable - to foretell them. whereas uncertainties, geological dangers and usual risks are usually pointed out in geological textbooks, meetings papers, and articles, no complete and systematic overview has up to now been tried. This ebook, written at an effectively refined point to accommodate complexity of those difficulties, offers an in depth overview of the total challenge, discussing it from either, the geological and the mathematical aspects.

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Extra info for Evaluation of Uncertainties and Risks in Geology: New Mathematical Approaches for their Handling

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Probability theory has to do with experiments that have a set of distinct outcomes. The experiment is not well-defined until we identify a set of outcomes (which can be infinite). The collection of all outcomes is called the sample space. Mathematically speaking, a sample space is a set and the outcomes are the elements of the set. We restrict ourselves to finite sample spaces in what follows. Then every subset of the sample space is called an event. A subset containing exactly one outcome is called an elementary event.

That is, can we come up with some mathematical entity that takes a (discrete) probability distribution and returns a number that can be interpreted as a measure of the uncertainty associated with that distribution. Let us proceed by considering what features such a measure should have. For concreteness, let X be a discrete random variable with finitely many possible values {Xl, X2, ... , x n }. The associated probabilities are denoted by P = {Pl,P2,'" ,Pn}. That is, Pi = P(X = Xi) for i = 1, ...

5 Dempster-Shafer Theory of Evidence 29 Focal elements represent propositions being directly supported by the given evidence encoded by m. No belief can ever be assigned to the false proposition (represented as 0). The focal elements and the associated bpa define a body of evidence. 4. Consider the following situation. A dice is thrown. The task is to encode the information given about the outcome of this experiment as a bpa m over the set U = {l, ... ,6} of possible results. g. "2", can be uniquely identified.

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Evaluation of Uncertainties and Risks in Geology: New Mathematical Approaches for their Handling by Professor Dr. György Bárdossy, Professor Dr. János Fodor (auth.)

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